What is the grammatical form of the sentence after the word "paradox"

Question

This is a sentence on the book "1100 Words You Need to Know" Week 1 Day 3. I can understand the meaning of the sentence perfectly but the sentence structure and grammatical rules are a bit weird for me after the word paradox.

Sylvia regularly took a crowded subway train to work during rush hour, so she found it to be a "paradox" one hot, steamy Tuesday to easily find a seat in a car that was nearly empty.

When we say "she found it to be a", we must use a noun or a noun phrase after "a" but is "paradox one hot, steamy Tuesday to easily find a seat in a car that was nearly empty" a noun phrase?

Shouldn't we say instead "she found it a paradox that in a hot, steamy Tuesday she could find a seat in a car that was nearly empty"?

----Edit ( I write the full text below. It may help )

Sylvia regularly took a crowded subway train to work during rush hour, so she found it to be a paradox one hot, steamy Tuesday to easily find a seat in a car that was nearly empty. She wondered how, in the realm of possibilities, this could be; how often in the annals of subway history had there been such a fortunate occurrence? To compound the puzzle, looking out the window she could see many commuters busily racing on the platform to fill other cars. It was not until she saw the sign on the door that she realized, with a tinge of resignation, why she had been so “lucky” this morning: “We apologize, but the air conditioning is not working in this car.”

Answer 1

Sylvia regularly took a crowded subway train to work during rush hour, so she found it to be a "paradox" one hot, steamy Tuesday to easily find a seat in a car that was nearly empty.

• 1. I would never have used the word paradox here. But never mind, the author did.
• 2. Don't be misled by: one hot, steamy Tuesday, which is adverbial (when she found it paradoxical) and could have been placed elsewhere:

In order to see how it works, we can write it like this:
[...] so she found it, one hot, steamy Tuesday, to be a "paradox" to easily find a seat in a car that was nearly empty.

• 3. to find something to be something
• 4. to easily find a seat in a car that was nearly empty.= a to-infinitive clause

AND:

1. First, the "it" is the rheme in the sentence, and the infinitive clause is the theme.

More about how that works here (very useful, by the way): theme/rheme construction

2. For me, the following would be grammatical:

• to find it to be a paradox that she was able to so easily find a seat.

3. • For me, this is ungrammatical or at the least very awkward:
     to find it to be a paradox to easily find a seat in a car.

Generally speaking, constructions with "to find it to be an x" with a theme/rheme construction sound awful when followed by a to-infinitive and are better structured with a subordinate clause.

• I find it to be a mistake that a sentence like this is given as an example to students.

And not:

• I find it to be a mistake to give a sentence like this as an example to students.

Better: I find giving a sentence like this as an example to students to be a mistake.

Using two to's there, at the very least, sounds awful.

Better: so she thought that finding a seat in a nearly empty car so easily on that hot steamy Tuesday was paradoxical.

Also, the repetition of "find something to be" and find a thing [seat] is also poor style.

Answer 2

Summarizing some of the comments:

I followed the link to the book. It seems to be a pretty popular book for cramming vocabulary for standardized entrance exams. It may work well if all you care about is learning the meanings of the words for a multiple choice test. Do not use it to learn English grammar or as a model for good writing.

The smallest fix I can think of for this single part of this particular sentence would be to say

... found it paradoxical that on one hot ...

Even that is only a partial fix. "Strange" or "surprising" would be a better word than "paradoxical".